Solve 4x - 0.35(x - 1) = 220.6 for x.

Step-by-step solution

1. 1

   Distribute before doing anything else. Removing the bracket correctly is the only real difficulty here:

   $4x-0.35(x-1)=4x-0.35x+0.35$

2. 2

   Combine into a single linear expression.

   $4x-0.35x=3.65x\quad\Rightarrow\quad 3.65x+0.35=220.6$

   The left side is now the standard form $mx+b$ with $m=3.65$ and $b=0.35$.

3. 3

   Move the constant across.

   $3.65x=220.6-0.35=220.25$

   Writing $220.6$ as $220.60$ first makes this subtraction hard to get wrong.

4. 4

   Divide, clearing the decimals first.

   $x=\frac{220.25}{3.65}=\frac{22025}{365}=\frac{4405}{73}$

   (Both numerator and denominator were multiplied by $100$, then divided by their common factor $5$.)

5. 5

   Express as a decimal and check. $73\cdot 60=4380$, remainder $25$, so $x=60+\frac{25}{73}=60.342466\ldots$ Substituting: $3.65\cdot 60.342466=220.25$, and $220.25+0.35=220.60$. The original equation holds, so $x=\frac{4405}{73}\approx 60.3425$.